Strong Gaussian Approximation of Constant Learning Rate SGD: Bias and Trajectory Inference
This paper develops strong Gaussian approximations (KMT type) for constant learning rate stochastic gradient descent (SGD). We work with heavy tailed noise and assume that the number of iterates grows and the learning rate shrinks simultaneously. Our work constructs simple Gaussian processes on the same space and bounds, in probability, the maximum difference between the SGD errors and their respective limits. While there exist central limit theorems for constant rate SGD centered at the optimum, these only provide individual iterate inference. By contrast, our quenched KMT approximations allow for finite sample, simultaneous, whole-trajectory-level inference and imply stochastic process ...
| Authors | Joseph Keslin, Wei Biao Wu |
|---|---|
| Primary category | stat.ML |
| Published | 10 October 2026 |
| Last updated at source | 14 October 2026 |
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